Vlad Serban
Visiting Associate Professor in Mathematics
Bio
I am a visiting faculty in Mathematics at New College of Florida.
Previously, I was a postdoc at EPFL working with Prof. Maryna Viazovska. My research interests lie in algebraic number theory and a good chunk of my work is related to p-adic aspects of the Langlands programme. I also enjoy thinking about how to apply ideas from arithmetic to various optimization problems such as producing good codes and sphere packings and have recently been studying lattices with additional arithmetic structure.
You can find some of my work below, stay tuned for upcoming work on p-adic L-functions and sphere packings.
Publications
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Moments of the number of points in a bounded set for number field lattices, with Nihar Gargava and Maryna Viazovska. arXiv:2308.15275
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Non-vanishing of critical L-values in Hida families, with Rob Pollack. arXiv:2208.02769
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Unlikely intersections on the p-adic formal ball. arXiv:2107.06610 Res. Number Theory (2023), vol. 9 (34), https://doi.org/10.1007/s40993-023-00441-1.
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Dense packings via lifts of codes to division rings, with Nihar Gargava. arXiv:2111.03684 IEEE Trans. Inform. Theory (2023), vol. 69, no. 5, pp. 2860-2873, https://doi.org/10.1109/TIT.2022.3226028.
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On p-adic versions of the Manin-Mumford Conjecture. arXiv:2007.02069 Int. Math. Res. Not. IMRN (2022), no.13, 10279-10301, https://doi.org/10.1093/imrn/rnab136.
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The Lang-Trotter conjecture for products of non-CM elliptic curves, with Hao Chen and Nathan Jones. arXiv:2006.11269 Ramanujan J. (2022), vol. 59, pp. 379-436, https://doi.org/10.1007/s11139-021-00543-3.
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A finiteness result for p-adic families of Bianchi modular forms. arXiv:1902.03217 J. Number Theory (2021), vol. 233, pp. 405-431, https://doi.org/10.1016/j.jnt.2021.06.016.
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An infinitesimal p-adic multiplicative Manin-Mumford Conjecture. arXiv:1607.01428 J. Théor. Nombres Bordeaux (2018), vol. 30, no.2, pp. 393-408, https://doi.org/10.5802/jtnb.1030.